The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

The numerical solution of linear elliptic partial differential equations most often involves a
finite element or finite difference discretization. To preserve sparsity, the arising system is …

Quasi-Newton-type iterative solvers are developed for a wide class of nonlinear elliptic
problems. The presented generalization of earlier efficient methods covers various …

We extend the theory of Sobolev gradients to include variable metric methods, such as
Newton's method and the Levenberg–Marquardt method, as gradient descent iterations …

Least squares methods are effective for solving systems of partial differential equations. In
the case of nonlinear systems the equations are usually linearized by a Newton iteration or …

A preconditioning framework is presented for the iterative solution of nonlinear elliptic
problems based on the preconditioning operator approach. Various fixed preconditioning …

The goal of this paper is to present various types of iterative solvers: gradient iteration,
Newton's method and a quasi-Newton method, for the finite element solution of elliptic …

Quasi‐Newton iterations are constructed for the finite element solution of small‐strain
nonlinear elasticity systems in 3D. The linearizations are based on spectral equivalence and …

The numerical solution of nonlinear elliptic transport systems is considered. An outer–inner
(damped inexact Newton plus PCG type) iteration is proposed for the finite element …

A mesh independent bound is given for the superlinear convergence of the CGM for
preconditioned self-adjoint linear elliptic problems using suitable equivalent operators. The …